On the Kinematics of Spiccato Bowing

Dept. for Speech, Music and Hearing Quarterly Progress and Status Report On the kinematics of spiccato bowing Guettler, K. and Askenfelt, A. journal: TMH-QPSR volume: 38 number: 2-3 year: 1997 pages: 047-052 http://www.speech.kth.se/qpsr TMH-QPSR 2-3/1997 On the kinematics of spiccato bowing Knut Guettler* and Anders Askenfelt * Norwegian State Academy of Music, Oslo, Norway Abstract A skilled string performer is able to play a series of spiccato notes (short strokes played by a bouncing bow) with each onset showing little or no aperiodic motion before a regular slip/stick pattern (Helmholtz motion) is triggered. Kinematic analysis reveals that a well-behaving bow gives nearly vertical impacts on the string, and that the first slip of each note takes place when the normal bow force is near its maximum. The complex movement of the bow stick can be decomposed into a translational and a rotational motion. Within one full cycle of the translational motion (down-up bow), giving two notes, the bow describes two periods of rotational motion. The axis of rotation is close to the finger grip at the frog. This paper discusses the relation between the quality of the spiccato and the phase lag between the two components of bow motion. Introduction π = Spiccato (from Italian spiccare: “clearly vB C1 sin t separated, cut off”) is a bowing technique in 30To which the player lets the bow bounce on the string – once per note – in order to create a series of notes with quick, crisp attacks followed by π fz = C2 + C3 cos t −α for fZ ≥ 0 else much longer, freely decaying “tails.” This effect 15To was not easily achieved until François Tourte = (1747-1835) designed a bow with concave fZ 0 curvature of the stick. This design was quite opposite to the earliest musical bows which had a where To is the fundamental period of the string. convex shape (bending away from the hair). In A maximum of 30 nominal periods is possible order to produce a crisp spiccato the bow force for each bow stroke. For α = 0 the note starts must be “switched on and off” very quickly. The with full force and zero velocity. As α is Tourte bow can manage this well because it does increased, the build-up in force is successively not tend to fold or collapse in contrast to the delayed, making it follow the increase in bow older types. However, a stiff bow alone is not velocity closer and closer (see Fig. 3). At a lag of enough to produce good-quality spiccato. A very α = 112° they will depart from zero simul- precise timing in the bow control is also taneously. imperative. In fact, the quality of the rapid Each note in Fig. 1 can be subdivided into spiccato differs greatly even among professional five phases (intervals a-b, b-c, etc.), all of which string players of today. are necessary for producing a crisp spiccato with clean attacks. After the initial release at (a), the The phases of a “perfect” spiccato string velocity curve shows regular Helmholtz Figure 1 shows a computer-simulated “perfect” triggering with one single slip per period. During spiccato as performed on an open violin G-string the interval (a-b), the string amplitude builds up (196 Hz). The main control parameters, the bow quickly until, at (b), the bow force has dropped so much that the string motion starts a free, velocity vB, and the bow force fZ are shown together with the obtained string velocity at the exponential decay. The decay rate is determined by the internal damping of the string and the point of excitation. The time history of vB is losses at the terminations. This state lasts until defined as a sine function (vB positive for down- (c), where f starts rising again, increasing the bows and negative for up-bows), and fZ as a half- Z rectified cosine function with an offset. The frictional force. Due to the lowered vB the bow is now braking the string, forcing a quick decay of frequency of fZ is twice the frequency of vB. The bow velocity and bow force were defined as the string velocity. At (d), the limiting static 47 Guettler & Askenfelt: On the kinetics of spiccato bowing Figure 1. The “perfect” spiccato can be subdivided in four phases (see text). Simulation of rapid spiccato on an open violin G-string. frictional force is high enough to prevent the string from slipping as the velocity passes zero Evaluation of the phase lag and changes direction. This silent part prepares Three simulated cases of spiccato with different the next string release which will take place in amount of phase lag (α) between bow velocity the opposite direction. and bow force are compared in Figure 3. In the Figure 2 shows the two components of the upper graph, the force function is applied without bow motion which are necessary to create the any lag (α = 0). This leads to a situation where desired combination of vB and fZ. The straight the bow force decreases far too early so that arrow at the frog indicates a translational when maximum velocity is reached, the force has movement with the frequency of vB. At the tip, a already gone down to zero. Further, the force rotational movement is indicated. The centre of starts its second increase long before vB has this rotation lies somewhere at the frog, close to descended to a low value. In all, this results in a the position of the player’s thumb. The frequency double build-up of each note. The string of the rotational motion is that of fZ, twice the amplitude will never reach a high value and the frequency of the translational motion. For the perceptual impression is a “choked” spiccato. player, the challenge lies in the phase co- In the middle graph, fZ is given a lag of 53° ordination of these two components, as will be compared to the velocity. This produces the illustrated in the next section. “perfect” spiccato which was shown in Figure 1. In the lower graph the lag is 107°. Of the four notes in this latter series, two are “scratchy” with multiple flybacks attacks and irregular and poorly defined onsets (#2 and #3). The two remaining notes show clearly longer build-up times than in the perfect case. The explanation should primarily be sought in the lack of forced damping which precedes the initial slips in the Figure 2. During spiccato, the movement of the perfect case (middle graph). For large lags as in bow can be decomposed into a translational and this latter case (α = 107°), remaining Helmholtz a rotational motion. The centre of rotation lies close to the player's thumb at the frog. components from the preceding note with high 48 TMH-QPSR 2-3/1997 Figure 4. Power output obtained in nine spiccato simulations with different timing between bow velocity and bow force. Each simulation consisted of 30 notes. The values are given as the arithmetic average of the decibel values of harmonics 2 through 20 (squares) compared to the power of the 1st harmonic (circles). The last three simulations on the right-hand (noisy) side included many “scratchy” attacks that appeared randomly in spite of the consistent control of the bowing parameters (bow velocity and bow force). Figure 3. Computer simulations of spiccato with sounded choked, but less so as the “optimal” lag three different phase lags (α = 0, 53°, and of 53° was approached. 107°) of the bow force (dashed line) relative to Figure 4 shows an estimation of the output the bow-velocity (white line). Only the middle power, given as the arithmetic average of the case produces a “perfect” spiccato. decibel values of harmonics 2 through 20 compared to the power of the 1st harmonic. Not sur- amplitudes and “wrong (opposite) phase orien- prisingly, the “perfect” spiccato gives the highest tation are still present on the string when vB 1st-harmonic power, while α = 107° gives the changes sign. highest average power for the partials. The graphs in Figure 3 were taken from a The results of the simulations do not imply simulation series with nine sets – each consisting that α = 53° is a magic figure. The “magic” lies of 30 notes – in which α was changed from 0° to ° ° elsewhere. A perfect attack requires a few initial 107 in steps of 13 . The force on the bridge was periods with a gradually increasing v combined taken as the output of the simulation, and B with a fZ that does not change too rapidly, say, convolved with a transfer function, relating the less than 5 - 7 % per nominal period. With the radiated sound to the bridge force. This transfer force-velocity lag of the perfect case (α = 53°, function was obtained by recording a force see Fig. 1), this leaves fZ with a relatively wide impact on a violin bridge and the resulting sound marginal of about ± 20 - 30° (cycle deg) around pressure at a distance of 30 cm from the violin its peak value, during which the initial periods body. This convolution gave a signal with the must be triggered. In Fig. 1, the first release characteristics of the sound of a real violin, and occurred 9° after the force maximum. With a the quality of the spiccato could then be judged slightly higher vB the first release would have by listening. Out of the nine simulation sets, only occurred earlier, but perfect attacks might still one case produced perfect attacks for all 30 have been produced.

Load more